List of top Questions asked in KEAM- 2016

If y-intercept of the line $4x - ay = 8$ is thrice its x-intercept, then the value of $a$ is equal to:

If $\tan A - \tan B = x$ and $\cot B - \cot A = y$, then the expression for $\cot(A - B)$ is:

If $\tan^{-1} x + \tan^{-1} y = \frac{2\pi}{3}$, then the value of $\cot^{-1} x + \cot^{-1} y$ is equal to:

The value of \( x \) satisfying the equation \( \tan^{-1} x + \tan^{-1} \left(\frac{2}{3}\right) = \tan^{-1} \left(\frac{7}{4}\right) \) is:

If $A(2, 4)$ and $B(6, 10)$ are two fixed points and if a point $P$ moves so that $\angle APB$ is always a right angle, then the locus of $P$ is:

If the orthocenter, centroid, incenter and circumcentre coincide in a triangle $ABC$, and if the length of side $AB$ is $\sqrt{75}$ units, then the length of the altitude of the triangle through the vertex $A$ is:

If \( \tan \theta = \frac{1}{2} \) and \( \tan \phi = \frac{1}{3} \), then the value of \( \tan(2\theta + \phi) \) is:

If \( p : 3 \) is a prime number and \( q : \text{one plus one is three} \), then the compound statement “It is not that 3 is a prime number or it is not that one plus one is three” is:

The value of \( \sin^2 \frac{\pi}{8} + \sin^2 \frac{3\pi}{8} + \sin^2 \frac{5\pi}{8} + \sin^2 \frac{7\pi}{8} \) is equal to:

If \( \sin x + \cos x = \sqrt{2} \), then the value of \( \sin x \cos x \) is equal to:

The value of \( \frac{\sqrt{3}}{\sin 15^\circ} - \frac{1}{\cos 15^\circ} \) is equal to:

Let \( p : 57 \) is an odd prime number,
\( q : 4 \) is a divisor of 12,
\( r : 15 \) is the LCM of 3 and 5 be three simple logical statements.
Which one of the following is true?

The least integer satisfying \( \frac{396}{10} - \frac{19-x}{10}<\frac{376}{10} - \frac{19-9x}{10} \) is:

Let \( p, q, r \) be three simple statements. Then \( \sim(p \lor q) \lor \sim(p \lor r) \equiv \)

Let \( A = \begin{bmatrix} 1 & \frac{-1-i\sqrt{3}}{2} \\ \frac{-1+i\sqrt{3}}{2} & 1 \end{bmatrix} \). Then \( A^{100} \) is equal to:

If \( |x-1| + |x-3| \leq 8 \), then the values of \( x \) lie in the interval:

If \( A = \begin{vmatrix} 8 & 27 & 125 \\ 2 & 3 & 5 \\ 1 & 1 & 1 \end{vmatrix} \), then the value of \( A^2 \) is equal to:

If \( A = \begin{bmatrix} x & 1 & -x \\ 0 & 1 & -1 \\ x & 0 & 7 \end{bmatrix} \) and \( \det(A) = \begin{vmatrix} 3 & 0 & 1 \\ 2 & -1 & 2 \\ 0 & 0 & 3 \end{vmatrix} \), then the value of \( x \) is:

The coefficient of \( x^2 \) in the expansion of the determinant \( \begin{vmatrix} x^2 & x^3+1 & x^5+2 \\ x^3+3 & x^2+x & x^3+x^4 \\ x+4 & x^3+x^5 & 2^3 \end{vmatrix} \) is:

If \( \begin{bmatrix} 1 & x & 1 \end{bmatrix} \begin{bmatrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 2 & 0 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = 0 \), then the values of \( x \) are:

The hybridized state of Al\(^{3+}\) in the complex ion formed when AlCl\(_3\) is treated with aqueous acid is

In which one of the following compounds of xenon, highest number of lone pairs of electrons is present on xenon?

The second ionization enthalpy of which of the following alkaline earth metals is the highest?

Which one of the following group 16 elements does not exist in -2 oxidation state?

The low solubility of LiF and that of CsI in water are respectively due to which of the properties of the alkali metal ions?